The conflict threatens to continue when the two face each other in Parliament this week, spooking investors who fear that crucial economic policies that would make doing business in India less cumbersome could become the victim of the fight.

Congress has also ratcheted-up pressure on the government over an investigation into allegations of graft by a government examination board, known by its Hindi acronym Vyapam, in the BJP-run state of Madhya Pradesh that is now part of a federal law enforcement probe.

Congress says Prime Minister Modi must explain his colleagues’ alleged role in these matters or ask them to resign. They have also vowed to protest in Parliament and prevent any discussion or votes on pending bills.

Ms. Swaraj and Ms. Raje Scindia have denied wrongdoing and have not resigned. The BJP has so far given them its support. The prime minister has not commented publically on the matter.

Madhya Pradesh’s chief minister, Shivraj Chouhan, has said the state supports a thorough investigation into the case.

With alleged corruption scandals dominating the news agenda at a time when Mr. Modi and his ministers are scouting for money in India and overseas, Singapore-based DBS Group warned in a note Monday that a failure to get crucial bills through Parliament this session “will be negative for market sentiment.”

Opposition parties have united to block the changes, calling them “anti-farmer.”

Mr. Modi came to power in 2014 with the first lower-house parliamentary majority in 30 years. But his party’s majority does not extend to the upper house of Parliament, or the Rajya Sabha, where opposition parties hold the balance of power.

Struggling to build a consensus, the government has pushed its proposals through executive orders, without a parliamentary vote, three times. Such ordinances needs to be approved by Parliament to become permanent law.

BJP leaders said a few months ago that the party was willing to consider a joint session of Parliament, which would help Mr. Modi override an upper-house no-vote, to pass the law. But ahead of the monsoon session, the government appears more willing to broker a compromise or even pull back.

In the most-recent session of Parliament, the proposed changes to the land-acquisition law were referred to a committee whose report will be the basis of parliamentary discussion and vote. But the report is delayed and is only likely to be ready mid-way through the session. Mr. Jaitley also suggested last week that if the government fails to get its political opponents on board, the central government may back down and leave it to individual state governments to make the amendments if they so choose.

Corruption allegations, policy unpredictability and disruptions in Parliament: Indians could be excused for thinking that the clock has turned back three years. Except this time, it’s the BJP rather than Congress under scrutiny.

Indeed, Congress leaders learned the trick of parliamentary disruption from the BJP.

In the final two years of the Congress-led government’s tenure to May 2014, the BJP repeatedly stalled Parliament over corruption allegations. Mr. Jaitley said then, when he was a senior opposition leader, that obstructing Parliament was a legitimate form of protest in a democracy.

In the five parliamentary sessions from 2012 to 2014, productivity tanked to an average of 44%, delaying and sometimes derailing Congress’s agenda. Productivity is measured by whether sessions last their allotted times.

But, with the boot firmly on the other foot, Congress now senses an opportunity to stall Mr. Modi in the upcoming 18-day sitting and is set on preventing Parliament from working.

The difference with Congress’s obstructionism, however, is that the party was stymied in the twilight years of its decade-long run. Congress has begun its offensive at the start of Mr. Modi’s five-year tenure, imperiling his agenda early on and raising questions over how far he will be able to take his ambitious plans.

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India Real Time offers analysis and insights into the broad range of developments in business, markets, the economy, politics, culture, sports, and entertainment that take place every single day in the world’s largest democracy. Regular posts from Wall Street Journal and Dow Jones Newswires reporters around the country provide a unique take on the main stories in the news, shed light on what else mattered and why, and give global readers a snapshot of what Indians have been talking about all week. You can contact the editors at indiarealtime(at)wsj(dot)com.